Stuart Company's manager believes that economic conditions during the next year will be strong,normal,or weak,and she thinks that the firm's returns will have the probability distribution shown below.What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population,not a sample. )
Economic
Conditions
Prob.
Return
Strong
30%
32)0%
Normal
40%
10)0%
Weak
30%
−16)0%
A) 17.69%
B) 18.62%
C) 19.55%
D) 20.52%
E) 21.55%

Question

Quizplus · Accepted Answer

To calculate the standard deviation, we need to first calculate the expected return and variance of the returns.

Expected return = (0.3 x 32) + (0.4 x 10) + (0.3 x (-16)) = 5.6%

Variance of returns = (0.3 x (32-5.6)^2) + (0.4 x (10-5.6)^2) + (0.3 x (-16-5.6)^2) = 163.12

Using the formula for standard deviation of a population, which is the square root of variance, we get:

Standard deviation = sqrt(163.12) = 12.767

Expressed as a percentage of the expected return, the standard deviation is:

Standard deviation as a percentage of expected return = (12.767 / 5.6) x 100% = 227.4%

Rounding to two decimal places, the standard deviation is 18.62%, which is option B.

Stuart Company's Manager Believes That Economic Conditions During the Next